Applying Reinforcement Learning to Option Pricing and Hedging

ArXiv ID: 2310.04336 “View on arXiv”

Authors: Unknown

Abstract

This thesis provides an overview of the recent advances in reinforcement learning in pricing and hedging financial instruments, with a primary focus on a detailed explanation of the Q-Learning Black Scholes approach, introduced by Halperin (2017). This reinforcement learning approach bridges the traditional Black and Scholes (1973) model with novel artificial intelligence algorithms, enabling option pricing and hedging in a completely model-free and data-driven way. This paper also explores the algorithm’s performance under different state variables and scenarios for a European put option. The results reveal that the model is an accurate estimator under different levels of volatility and hedging frequency. Moreover, this method exhibits robust performance across various levels of option’s moneyness. Lastly, the algorithm incorporates proportional transaction costs, indicating diverse impacts on profit and loss, affected by different statistical properties of the state variables.

Keywords: Q-Learning Black Scholes, Reinforcement learning, Option pricing, Hedging, Proportional transaction costs, Options / Derivatives

Complexity vs Empirical Score

• Math Complexity: 7.5/10
• Empirical Rigor: 4.0/10
• Quadrant: Lab Rats
• Why: The paper introduces advanced RL concepts (Q-learning, FQI, offline RL) and mathematical formalisms (MDPs, transition probabilities) which are dense for finance literature, but the testing is limited to theoretical scenarios on European puts without live market data, code, or robust backtesting metrics.

  flowchart TD
    A["Research Goal:<br/>Model-Free Option Pricing & Hedging with RL"] --> B["Core Methodology:<br/>Q-Learning Black-Scholes Framework"]
    B --> C{"Data/Input: European Put Option<br/>Variables: Spot Price, Strike, Volatility"}
    C --> D["Computational Process:<br/>Q-Value Approximation & Policy Optimization"]
    D --> E{"Incorporation of<br/>Proportional Transaction Costs?"}
    E -- Yes --> F["Simulated P&L Analysis"]
    E -- No --> G["Simulated P&L Analysis"]
    F & G --> H["Key Outcomes:<br/>Accurate Estimation<br/>Robust to Volatility/Moneyness<br/>Transaction Costs Impact P&L"]